Theorems · Theorem · group theory
finprod_eq_prod_plift_of_mulSupport_subset
∀ {M : Type u_2} {α : Sort u_4} [inst : CommMonoid M] {f : α → M} {s : Finset (PLift α)},
Function.mulSupport (f ∘ PLift.down) ⊆ ↑s → ∏ᶠ (i : α), f i = ∏ i ∈ s, f i.down- Defined in
- Mathlib.Algebra.BigOperators.Finprod
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Finset.prodstatement · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Set.Finite.toFinsetproof · cited by 351
- Set.Finite.subsetproof · cited by 285
- finprodstatement · cited by 257
- Function.mulSupportstatement and proof · cited by 240
- Finset.finite_toSetproof · cited by 210
- Set.Finite.mem_toFinsetproof · cited by 74
- finprod_eq_prod_plift_of_mulSupport_toFinset_subsetproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- finprod_eq_prod_of_mulSupport_subsetproof · cited by 21
- finprod_oneproof · cited by 12
- MonoidHom.map_finprod_pliftproof · cited by 3
- finprod_eq_singleproof · cited by 1
- smul_finprod'proof · cited by 0